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GF Casting Solutions is a development partner and manufacturer of lightweight cast components made of ductile iron, aluminum and magnesium for the automotive industry as well as a variety of industrial applications. GF Casting Solutions manufactures at 14 production sites in Germany, Austria, Romania, Switzerland, China and the USA.
Elements of GF(p n) may be represented as polynomials of degree strictly less than n over GF(p). Operations are then performed modulo m(x) where m(x) is an irreducible polynomial of degree n over GF(p), for instance using polynomial long division. Addition is the usual addition of polynomials, but the coefficients are reduced modulo p.
Let L = GF(q n) be a finite extension of a finite field K = GF(q).Since L/K is a Galois extension, if α is in L, then the trace of α is the sum of all the Galois conjugates of α, i.e. [4]
In finite field theory, a branch of mathematics, a primitive polynomial is the minimal polynomial of a primitive element of the finite field GF(p m).This means that a polynomial F(X) of degree m with coefficients in GF(p) = Z/pZ is a primitive polynomial if it is monic and has a root α in GF(p m) such that {,,,,, …} is the entire field GF(p m).
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules.
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Let α be a primitive element of GF(q m). For any positive integer i, let m i (x) be the minimal polynomial with coefficients in GF(q) of α i. The generator polynomial of the BCH code is defined as the least common multiple g(x) = lcm(m 1 (x),…,m d − 1 (x)). It can be seen that g(x) is a polynomial with coefficients in GF(q) and divides x ...
The definition of the Gibbs function is = + where H is the enthalpy defined by: = +. Taking differentials of each definition to find dH and dG, then using the fundamental thermodynamic relation (always true for reversible or irreversible processes): = where S is the entropy, V is volume, (minus sign due to reversibility, in which dU = 0: work other than pressure-volume may be done and is equal ...
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